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11.47 (1990)

Solved

Let $L_d$ be the homogeneous component of degree $d$ in a free Lie algebra $L$ of rank 2 over the field of order 2. What is the dimension of the fixed point space in $L_d$ for the automorphism of $L$ which interchanges two elements of a free generating set of $L$?

Contributor: L. G. Kovács

Progress

It is found; R. M. Bryant and R. Stöhr (Arch. Math., 67, no. 4 (1996), 281–289) confirmed the conjecture from (M. W. Short, Commun. Algebra, 23, no. 8 (1995), 3051–3057).

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